TSTP Solution File: LCL488+1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL488+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sun Jul 17 12:52:36 EDT 2022
% Result : Theorem 0.61s 0.79s
% Output : CNFRefutation 0.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 26
% Syntax : Number of formulae : 121 ( 60 unt; 0 def)
% Number of atoms : 214 ( 76 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 174 ( 81 ~; 71 |; 9 &)
% ( 8 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 12 ( 9 usr; 9 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 8 con; 0-2 aty)
% Number of variables : 183 ( 9 sgn 46 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(modus_ponens,axiom,
( modus_ponens
<=> ! [X,Y] :
( ( is_a_theorem(X)
& is_a_theorem(implies(X,Y)) )
=> is_a_theorem(Y) ) ) ).
fof(and_2,axiom,
( and_2
<=> ! [X,Y] : is_a_theorem(implies(and(X,Y),Y)) ) ).
fof(r2,axiom,
( r2
<=> ! [P,Q] : is_a_theorem(implies(Q,or(P,Q))) ) ).
fof(r3,axiom,
( r3
<=> ! [P,Q] : is_a_theorem(implies(or(P,Q),or(Q,P))) ) ).
fof(op_or,axiom,
( op_or
=> ! [X,Y] : or(X,Y) = not(and(not(X),not(Y))) ) ).
fof(op_and,axiom,
( op_and
=> ! [X,Y] : and(X,Y) = not(or(not(X),not(Y))) ) ).
fof(op_implies_and,axiom,
( op_implies_and
=> ! [X,Y] : implies(X,Y) = not(and(X,not(Y))) ) ).
fof(op_implies_or,axiom,
( op_implies_or
=> ! [X,Y] : implies(X,Y) = or(not(X),Y) ) ).
fof(principia_op_implies_or,axiom,
op_implies_or ).
fof(principia_op_and,axiom,
op_and ).
fof(principia_modus_ponens,axiom,
modus_ponens ).
fof(principia_r2,axiom,
r2 ).
fof(principia_r3,axiom,
r3 ).
fof(hilbert_op_or,axiom,
op_or ).
fof(hilbert_op_implies_and,axiom,
op_implies_and ).
fof(hilbert_and_2,conjecture,
and_2 ).
fof(subgoal_0,plain,
and_2,
inference(strip,[],[hilbert_and_2]) ).
fof(negate_0_0,plain,
~ and_2,
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
( ~ and_2
<=> ? [X,Y] : ~ is_a_theorem(implies(and(X,Y),Y)) ),
inference(canonicalize,[],[and_2]) ).
fof(normalize_0_1,plain,
! [X,Y] :
( ( ~ and_2
| is_a_theorem(implies(and(X,Y),Y)) )
& ( ~ is_a_theorem(implies(and(skolemFOFtoCNF_X_7,skolemFOFtoCNF_Y_7),skolemFOFtoCNF_Y_7))
| and_2 ) ),
inference(clausify,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
( ~ is_a_theorem(implies(and(skolemFOFtoCNF_X_7,skolemFOFtoCNF_Y_7),skolemFOFtoCNF_Y_7))
| and_2 ),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
~ and_2,
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_4,plain,
( ~ r2
<=> ? [P,Q] : ~ is_a_theorem(implies(Q,or(P,Q))) ),
inference(canonicalize,[],[r2]) ).
fof(normalize_0_5,plain,
! [P,Q] :
( ( ~ is_a_theorem(implies(skolemFOFtoCNF_Q_4,or(skolemFOFtoCNF_P_7,skolemFOFtoCNF_Q_4)))
| r2 )
& ( ~ r2
| is_a_theorem(implies(Q,or(P,Q))) ) ),
inference(clausify,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [P,Q] :
( ~ r2
| is_a_theorem(implies(Q,or(P,Q))) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
r2,
inference(canonicalize,[],[principia_r2]) ).
fof(normalize_0_8,plain,
( ~ op_or
| ! [X,Y] : or(X,Y) = not(and(not(X),not(Y))) ),
inference(canonicalize,[],[op_or]) ).
fof(normalize_0_9,plain,
! [X,Y] :
( ~ op_or
| or(X,Y) = not(and(not(X),not(Y))) ),
inference(clausify,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
op_or,
inference(canonicalize,[],[hilbert_op_or]) ).
fof(normalize_0_11,plain,
( ~ op_implies_and
| ! [X,Y] : implies(X,Y) = not(and(X,not(Y))) ),
inference(canonicalize,[],[op_implies_and]) ).
fof(normalize_0_12,plain,
! [X,Y] :
( ~ op_implies_and
| implies(X,Y) = not(and(X,not(Y))) ),
inference(clausify,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
op_implies_and,
inference(canonicalize,[],[hilbert_op_implies_and]) ).
fof(normalize_0_14,plain,
( ~ op_implies_or
| ! [X,Y] : implies(X,Y) = or(not(X),Y) ),
inference(canonicalize,[],[op_implies_or]) ).
fof(normalize_0_15,plain,
! [X,Y] :
( ~ op_implies_or
| implies(X,Y) = or(not(X),Y) ),
inference(clausify,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
op_implies_or,
inference(canonicalize,[],[principia_op_implies_or]) ).
fof(normalize_0_17,plain,
( ~ r3
<=> ? [P,Q] : ~ is_a_theorem(implies(or(P,Q),or(Q,P))) ),
inference(canonicalize,[],[r3]) ).
fof(normalize_0_18,plain,
! [P,Q] :
( ( ~ is_a_theorem(implies(or(skolemFOFtoCNF_P_8,skolemFOFtoCNF_Q_5),or(skolemFOFtoCNF_Q_5,skolemFOFtoCNF_P_8)))
| r3 )
& ( ~ r3
| is_a_theorem(implies(or(P,Q),or(Q,P))) ) ),
inference(clausify,[],[normalize_0_17]) ).
fof(normalize_0_19,plain,
! [P,Q] :
( ~ r3
| is_a_theorem(implies(or(P,Q),or(Q,P))) ),
inference(conjunct,[],[normalize_0_18]) ).
fof(normalize_0_20,plain,
r3,
inference(canonicalize,[],[principia_r3]) ).
fof(normalize_0_21,plain,
( ~ modus_ponens
<=> ? [X,Y] :
( ~ is_a_theorem(Y)
& is_a_theorem(X)
& is_a_theorem(implies(X,Y)) ) ),
inference(canonicalize,[],[modus_ponens]) ).
fof(normalize_0_22,plain,
! [X,Y] :
( ( ~ is_a_theorem(skolemFOFtoCNF_Y)
| modus_ponens )
& ( is_a_theorem(implies(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| modus_ponens )
& ( is_a_theorem(skolemFOFtoCNF_X)
| modus_ponens )
& ( ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y))
| ~ modus_ponens
| is_a_theorem(Y) ) ),
inference(clausify,[],[normalize_0_21]) ).
fof(normalize_0_23,plain,
! [X,Y] :
( ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y))
| ~ modus_ponens
| is_a_theorem(Y) ),
inference(conjunct,[],[normalize_0_22]) ).
fof(normalize_0_24,plain,
modus_ponens,
inference(canonicalize,[],[principia_modus_ponens]) ).
fof(normalize_0_25,plain,
( ~ op_and
| ! [X,Y] : and(X,Y) = not(or(not(X),not(Y))) ),
inference(canonicalize,[],[op_and]) ).
fof(normalize_0_26,plain,
! [X,Y] :
( ~ op_and
| and(X,Y) = not(or(not(X),not(Y))) ),
inference(clausify,[],[normalize_0_25]) ).
fof(normalize_0_27,plain,
op_and,
inference(canonicalize,[],[principia_op_and]) ).
cnf(refute_0_0,plain,
( ~ is_a_theorem(implies(and(skolemFOFtoCNF_X_7,skolemFOFtoCNF_Y_7),skolemFOFtoCNF_Y_7))
| and_2 ),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
~ and_2,
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_2,plain,
~ is_a_theorem(implies(and(skolemFOFtoCNF_X_7,skolemFOFtoCNF_Y_7),skolemFOFtoCNF_Y_7)),
inference(resolve,[$cnf( and_2 )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
( ~ r2
| is_a_theorem(implies(Q,or(P,Q))) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_4,plain,
r2,
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_5,plain,
is_a_theorem(implies(Q,or(P,Q))),
inference(resolve,[$cnf( r2 )],[refute_0_4,refute_0_3]) ).
cnf(refute_0_6,plain,
is_a_theorem(implies(not(X_9),or(P,not(X_9)))),
inference(subst,[],[refute_0_5:[bind(Q,$fot(not(X_9)))]]) ).
cnf(refute_0_7,plain,
( ~ op_or
| or(X,Y) = not(and(not(X),not(Y))) ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_8,plain,
op_or,
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_9,plain,
or(X,Y) = not(and(not(X),not(Y))),
inference(resolve,[$cnf( op_or )],[refute_0_8,refute_0_7]) ).
cnf(refute_0_10,plain,
( ~ op_implies_and
| implies(X,Y) = not(and(X,not(Y))) ),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_11,plain,
op_implies_and,
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_12,plain,
implies(X,Y) = not(and(X,not(Y))),
inference(resolve,[$cnf( op_implies_and )],[refute_0_11,refute_0_10]) ).
cnf(refute_0_13,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_14,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_15,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
( implies(X,Y) != not(and(X,not(Y)))
| not(and(X,not(Y))) = implies(X,Y) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(implies(X,Y))),bind(Y0,$fot(not(and(X,not(Y)))))]]) ).
cnf(refute_0_17,plain,
not(and(X,not(Y))) = implies(X,Y),
inference(resolve,[$cnf( $equal(implies(X,Y),not(and(X,not(Y)))) )],[refute_0_12,refute_0_16]) ).
cnf(refute_0_18,plain,
not(and(not(X),not(Y))) = implies(not(X),Y),
inference(subst,[],[refute_0_17:[bind(X,$fot(not(X)))]]) ).
cnf(refute_0_19,plain,
( not(and(not(X),not(Y))) != implies(not(X),Y)
| or(X,Y) != not(and(not(X),not(Y)))
| or(X,Y) = implies(not(X),Y) ),
introduced(tautology,[equality,[$cnf( $equal(or(X,Y),not(and(not(X),not(Y)))) ),[1],$fot(implies(not(X),Y))]]) ).
cnf(refute_0_20,plain,
( or(X,Y) != not(and(not(X),not(Y)))
| or(X,Y) = implies(not(X),Y) ),
inference(resolve,[$cnf( $equal(not(and(not(X),not(Y))),implies(not(X),Y)) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
or(X,Y) = implies(not(X),Y),
inference(resolve,[$cnf( $equal(or(X,Y),not(and(not(X),not(Y)))) )],[refute_0_9,refute_0_20]) ).
cnf(refute_0_22,plain,
or(X_9,or(P,not(X_9))) = implies(not(X_9),or(P,not(X_9))),
inference(subst,[],[refute_0_21:[bind(X,$fot(X_9)),bind(Y,$fot(or(P,not(X_9))))]]) ).
cnf(refute_0_23,plain,
( or(X_9,or(P,not(X_9))) != implies(not(X_9),or(P,not(X_9)))
| implies(not(X_9),or(P,not(X_9))) = or(X_9,or(P,not(X_9))) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(or(X_9,or(P,not(X_9))))),bind(Y0,$fot(implies(not(X_9),or(P,not(X_9)))))]]) ).
cnf(refute_0_24,plain,
implies(not(X_9),or(P,not(X_9))) = or(X_9,or(P,not(X_9))),
inference(resolve,[$cnf( $equal(or(X_9,or(P,not(X_9))),implies(not(X_9),or(P,not(X_9)))) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
( implies(not(X_9),or(P,not(X_9))) != or(X_9,or(P,not(X_9)))
| ~ is_a_theorem(implies(not(X_9),or(P,not(X_9))))
| is_a_theorem(or(X_9,or(P,not(X_9)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(not(X_9),or(P,not(X_9)))) ),[0],$fot(or(X_9,or(P,not(X_9))))]]) ).
cnf(refute_0_26,plain,
( ~ is_a_theorem(implies(not(X_9),or(P,not(X_9))))
| is_a_theorem(or(X_9,or(P,not(X_9)))) ),
inference(resolve,[$cnf( $equal(implies(not(X_9),or(P,not(X_9))),or(X_9,or(P,not(X_9)))) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
is_a_theorem(or(X_9,or(P,not(X_9)))),
inference(resolve,[$cnf( is_a_theorem(implies(not(X_9),or(P,not(X_9)))) )],[refute_0_6,refute_0_26]) ).
cnf(refute_0_28,plain,
is_a_theorem(or(X_9,or(not(X_17),not(X_9)))),
inference(subst,[],[refute_0_27:[bind(P,$fot(not(X_17)))]]) ).
cnf(refute_0_29,plain,
( ~ op_implies_or
| implies(X,Y) = or(not(X),Y) ),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_30,plain,
op_implies_or,
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_31,plain,
implies(X,Y) = or(not(X),Y),
inference(resolve,[$cnf( op_implies_or )],[refute_0_30,refute_0_29]) ).
cnf(refute_0_32,plain,
implies(X_17,not(X_9)) = or(not(X_17),not(X_9)),
inference(subst,[],[refute_0_31:[bind(X,$fot(X_17)),bind(Y,$fot(not(X_9)))]]) ).
cnf(refute_0_33,plain,
( implies(X_17,not(X_9)) != or(not(X_17),not(X_9))
| or(not(X_17),not(X_9)) = implies(X_17,not(X_9)) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(implies(X_17,not(X_9)))),bind(Y0,$fot(or(not(X_17),not(X_9))))]]) ).
cnf(refute_0_34,plain,
or(not(X_17),not(X_9)) = implies(X_17,not(X_9)),
inference(resolve,[$cnf( $equal(implies(X_17,not(X_9)),or(not(X_17),not(X_9))) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
( or(not(X_17),not(X_9)) != implies(X_17,not(X_9))
| ~ is_a_theorem(or(X_9,or(not(X_17),not(X_9))))
| is_a_theorem(or(X_9,implies(X_17,not(X_9)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(X_9,or(not(X_17),not(X_9)))) ),[0,1],$fot(implies(X_17,not(X_9)))]]) ).
cnf(refute_0_36,plain,
( ~ is_a_theorem(or(X_9,or(not(X_17),not(X_9))))
| is_a_theorem(or(X_9,implies(X_17,not(X_9)))) ),
inference(resolve,[$cnf( $equal(or(not(X_17),not(X_9)),implies(X_17,not(X_9))) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
is_a_theorem(or(X_9,implies(X_17,not(X_9)))),
inference(resolve,[$cnf( is_a_theorem(or(X_9,or(not(X_17),not(X_9)))) )],[refute_0_28,refute_0_36]) ).
cnf(refute_0_38,plain,
is_a_theorem(or(X_259,implies(X_17,not(X_259)))),
inference(subst,[],[refute_0_37:[bind(X_9,$fot(X_259))]]) ).
cnf(refute_0_39,plain,
( ~ r3
| is_a_theorem(implies(or(P,Q),or(Q,P))) ),
inference(canonicalize,[],[normalize_0_19]) ).
cnf(refute_0_40,plain,
r3,
inference(canonicalize,[],[normalize_0_20]) ).
cnf(refute_0_41,plain,
is_a_theorem(implies(or(P,Q),or(Q,P))),
inference(resolve,[$cnf( r3 )],[refute_0_40,refute_0_39]) ).
cnf(refute_0_42,plain,
( ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y))
| ~ modus_ponens
| is_a_theorem(Y) ),
inference(canonicalize,[],[normalize_0_23]) ).
cnf(refute_0_43,plain,
modus_ponens,
inference(canonicalize,[],[normalize_0_24]) ).
cnf(refute_0_44,plain,
( ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y))
| is_a_theorem(Y) ),
inference(resolve,[$cnf( modus_ponens )],[refute_0_43,refute_0_42]) ).
cnf(refute_0_45,plain,
( ~ is_a_theorem(implies(or(P,Q),or(Q,P)))
| ~ is_a_theorem(or(P,Q))
| is_a_theorem(or(Q,P)) ),
inference(subst,[],[refute_0_44:[bind(X,$fot(or(P,Q))),bind(Y,$fot(or(Q,P)))]]) ).
cnf(refute_0_46,plain,
( ~ is_a_theorem(or(P,Q))
| is_a_theorem(or(Q,P)) ),
inference(resolve,[$cnf( is_a_theorem(implies(or(P,Q),or(Q,P))) )],[refute_0_41,refute_0_45]) ).
cnf(refute_0_47,plain,
( ~ is_a_theorem(or(X_259,implies(X_17,not(X_259))))
| is_a_theorem(or(implies(X_17,not(X_259)),X_259)) ),
inference(subst,[],[refute_0_46:[bind(P,$fot(X_259)),bind(Q,$fot(implies(X_17,not(X_259))))]]) ).
cnf(refute_0_48,plain,
is_a_theorem(or(implies(X_17,not(X_259)),X_259)),
inference(resolve,[$cnf( is_a_theorem(or(X_259,implies(X_17,not(X_259)))) )],[refute_0_38,refute_0_47]) ).
cnf(refute_0_49,plain,
or(implies(X_13,not(X_14)),Y) = implies(not(implies(X_13,not(X_14))),Y),
inference(subst,[],[refute_0_21:[bind(X,$fot(implies(X_13,not(X_14))))]]) ).
cnf(refute_0_50,plain,
( ~ op_and
| and(X,Y) = not(or(not(X),not(Y))) ),
inference(canonicalize,[],[normalize_0_26]) ).
cnf(refute_0_51,plain,
op_and,
inference(canonicalize,[],[normalize_0_27]) ).
cnf(refute_0_52,plain,
and(X,Y) = not(or(not(X),not(Y))),
inference(resolve,[$cnf( op_and )],[refute_0_51,refute_0_50]) ).
cnf(refute_0_53,plain,
( implies(X,Y) != or(not(X),Y)
| or(not(X),Y) = implies(X,Y) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(implies(X,Y))),bind(Y0,$fot(or(not(X),Y)))]]) ).
cnf(refute_0_54,plain,
or(not(X),Y) = implies(X,Y),
inference(resolve,[$cnf( $equal(implies(X,Y),or(not(X),Y)) )],[refute_0_31,refute_0_53]) ).
cnf(refute_0_55,plain,
or(not(X),not(Y)) = implies(X,not(Y)),
inference(subst,[],[refute_0_54:[bind(Y,$fot(not(Y)))]]) ).
cnf(refute_0_56,plain,
not(or(not(X),not(Y))) = not(or(not(X),not(Y))),
introduced(tautology,[refl,[$fot(not(or(not(X),not(Y))))]]) ).
cnf(refute_0_57,plain,
( not(or(not(X),not(Y))) != not(or(not(X),not(Y)))
| or(not(X),not(Y)) != implies(X,not(Y))
| not(or(not(X),not(Y))) = not(implies(X,not(Y))) ),
introduced(tautology,[equality,[$cnf( $equal(not(or(not(X),not(Y))),not(or(not(X),not(Y)))) ),[1,0],$fot(implies(X,not(Y)))]]) ).
cnf(refute_0_58,plain,
( or(not(X),not(Y)) != implies(X,not(Y))
| not(or(not(X),not(Y))) = not(implies(X,not(Y))) ),
inference(resolve,[$cnf( $equal(not(or(not(X),not(Y))),not(or(not(X),not(Y)))) )],[refute_0_56,refute_0_57]) ).
cnf(refute_0_59,plain,
not(or(not(X),not(Y))) = not(implies(X,not(Y))),
inference(resolve,[$cnf( $equal(or(not(X),not(Y)),implies(X,not(Y))) )],[refute_0_55,refute_0_58]) ).
cnf(refute_0_60,plain,
( and(X,Y) != not(or(not(X),not(Y)))
| not(or(not(X),not(Y))) != not(implies(X,not(Y)))
| and(X,Y) = not(implies(X,not(Y))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(and(X,Y),not(implies(X,not(Y)))) ),[0],$fot(not(or(not(X),not(Y))))]]) ).
cnf(refute_0_61,plain,
( and(X,Y) != not(or(not(X),not(Y)))
| and(X,Y) = not(implies(X,not(Y))) ),
inference(resolve,[$cnf( $equal(not(or(not(X),not(Y))),not(implies(X,not(Y)))) )],[refute_0_59,refute_0_60]) ).
cnf(refute_0_62,plain,
and(X,Y) = not(implies(X,not(Y))),
inference(resolve,[$cnf( $equal(and(X,Y),not(or(not(X),not(Y)))) )],[refute_0_52,refute_0_61]) ).
cnf(refute_0_63,plain,
and(X_13,X_14) = not(implies(X_13,not(X_14))),
inference(subst,[],[refute_0_62:[bind(X,$fot(X_13)),bind(Y,$fot(X_14))]]) ).
cnf(refute_0_64,plain,
( and(X_13,X_14) != not(implies(X_13,not(X_14)))
| not(implies(X_13,not(X_14))) = and(X_13,X_14) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(and(X_13,X_14))),bind(Y0,$fot(not(implies(X_13,not(X_14)))))]]) ).
cnf(refute_0_65,plain,
not(implies(X_13,not(X_14))) = and(X_13,X_14),
inference(resolve,[$cnf( $equal(and(X_13,X_14),not(implies(X_13,not(X_14)))) )],[refute_0_63,refute_0_64]) ).
cnf(refute_0_66,plain,
( not(implies(X_13,not(X_14))) != and(X_13,X_14)
| or(implies(X_13,not(X_14)),Y) != implies(not(implies(X_13,not(X_14))),Y)
| or(implies(X_13,not(X_14)),Y) = implies(and(X_13,X_14),Y) ),
introduced(tautology,[equality,[$cnf( $equal(or(implies(X_13,not(X_14)),Y),implies(not(implies(X_13,not(X_14))),Y)) ),[1,0],$fot(and(X_13,X_14))]]) ).
cnf(refute_0_67,plain,
( or(implies(X_13,not(X_14)),Y) != implies(not(implies(X_13,not(X_14))),Y)
| or(implies(X_13,not(X_14)),Y) = implies(and(X_13,X_14),Y) ),
inference(resolve,[$cnf( $equal(not(implies(X_13,not(X_14))),and(X_13,X_14)) )],[refute_0_65,refute_0_66]) ).
cnf(refute_0_68,plain,
or(implies(X_13,not(X_14)),Y) = implies(and(X_13,X_14),Y),
inference(resolve,[$cnf( $equal(or(implies(X_13,not(X_14)),Y),implies(not(implies(X_13,not(X_14))),Y)) )],[refute_0_49,refute_0_67]) ).
cnf(refute_0_69,plain,
or(implies(X_17,not(X_259)),X_259) = implies(and(X_17,X_259),X_259),
inference(subst,[],[refute_0_68:[bind(Y,$fot(X_259)),bind(X_13,$fot(X_17)),bind(X_14,$fot(X_259))]]) ).
cnf(refute_0_70,plain,
( or(implies(X_17,not(X_259)),X_259) != implies(and(X_17,X_259),X_259)
| ~ is_a_theorem(or(implies(X_17,not(X_259)),X_259))
| is_a_theorem(implies(and(X_17,X_259),X_259)) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(or(implies(X_17,not(X_259)),X_259)) ),[0],$fot(implies(and(X_17,X_259),X_259))]]) ).
cnf(refute_0_71,plain,
( ~ is_a_theorem(or(implies(X_17,not(X_259)),X_259))
| is_a_theorem(implies(and(X_17,X_259),X_259)) ),
inference(resolve,[$cnf( $equal(or(implies(X_17,not(X_259)),X_259),implies(and(X_17,X_259),X_259)) )],[refute_0_69,refute_0_70]) ).
cnf(refute_0_72,plain,
is_a_theorem(implies(and(X_17,X_259),X_259)),
inference(resolve,[$cnf( is_a_theorem(or(implies(X_17,not(X_259)),X_259)) )],[refute_0_48,refute_0_71]) ).
cnf(refute_0_73,plain,
is_a_theorem(implies(and(skolemFOFtoCNF_X_7,skolemFOFtoCNF_Y_7),skolemFOFtoCNF_Y_7)),
inference(subst,[],[refute_0_72:[bind(X_17,$fot(skolemFOFtoCNF_X_7)),bind(X_259,$fot(skolemFOFtoCNF_Y_7))]]) ).
cnf(refute_0_74,plain,
$false,
inference(resolve,[$cnf( is_a_theorem(implies(and(skolemFOFtoCNF_X_7,skolemFOFtoCNF_Y_7),skolemFOFtoCNF_Y_7)) )],[refute_0_73,refute_0_2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL488+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.12 % Command : metis --show proof --show saturation %s
% 0.13/0.33 % Computer : n006.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sun Jul 3 04:53:37 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.61/0.79 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.61/0.79
% 0.61/0.79 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.61/0.80
%------------------------------------------------------------------------------